Cut the tofu block in half and place side by side on an absorbent towel (microfiber works well) and wrap up. Then place something heavy on top, to help push out the excess moisture. Let rest for 20 min. Meanwhile, make the tofu marinade. Whisk all ingredients, except cornstarch, in a small bowl and set aside. Also, make the stir-fry sauce by whisking all the ingredients in a small bowl and set aside.

When the tofu is done resting, unwrap and cut it into 1" cubes. Add the cubes to a medium bowl and gently fold in the marinade to coat the tofu. All the marinade should absorb into the tofu in about 10 min. (stir occasionally). Place the tofu in a large bowl and fold in 1 Tbsp of cornstarch at a time (3 Tbsp total), evenly coat the cubes (coating will become goopy, that's OK). You can shake and toss the cubes on the bowl to help coat evenly.

Warm sesame and vegetable oil in a cast-iron skillet or non-stick pan over medium-high heat. Add tofu in an even layer and brown all sides, rotating with tongs. Once browned, turn off the heat and add green onion, sauce, and chilies (if using). With a rubber spatula, gently fold the tofu and sauce together, scraping the bottom of the pan. Serve over cooked rice and steamed broccoli, and sprinkle with sesame seeds.